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Provide Solution For  R.D. Sharma Maths Class 12 Chapter 30 Probaility  Exercise 30.5 Question 18 Maths Textbook Solution.

Answers (1)

Answer:\frac{67}{256}

Hint: You must know the rules of finding probability functions.

Given: Bag contains = (4W+5R+7B) balls

Solution

No. of white balls = 4

No. of black balls = 7

No. of red balls = 5

 

Total balls = 16

 

No. of ways in which 4 balls can be drawn from 16 balls=16C_{4}

Let A = getting at least two white balls = getting 2, 3, 4 white balls

No. of ways of choosing 2 white balls =4C_{2}\times 12C_{2}

No. of ways of choosing 3 white balls =4C_{3}\times 12C_{1}

No. of ways of choosing 4 white balls =4C_{4}\times 12C_{0}

\begin{aligned} &P(A)=\frac{4 C_{2} \times 12 C_{2}+4 C_{3} \times 12 C_{1}+4 C_{4} \times 12 C_{0}}{16 C_{4}} \\ &=\frac{4 !}{2 ! 2 !} \times \frac{12 !}{2 ! 10 !}+\frac{4 !}{3 !} \times \frac{12 !}{11 !}+\frac{4 !}{4 ! 0 !} \times \frac{12 !}{12 !} \\ &=\frac{16 !}{4 ! 2 !} \\ &=\frac{67}{256} \end{aligned}

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